17 August 2018 11:19:25 PM

JACOBI_EIGENVALUE_TEST
  C++ version
  Test the JACOBI_EIGENVALUE library.

TEST01
  For a symmetric matrix A,
  JACOBI_EIGENVALUE computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

  Input matrix A:

  Col:          0             1             2             3       
  Row

    0:            4           -30            60           -35  
    1:          -30           300          -675           420  
    2:           60          -675          1620         -1050  
    3:          -35           420         -1050           700  

  Number of iterations = 11
  Number of rotations  = 21

  Eigenvalues D:

         0:       0.166643
         1:        1.47805
         2:        37.1015
         3:        2585.25

  Eigenvector matrix V:

  Col:          0             1             2             3       
  Row

    0:     0.792608      0.582076      0.179186     0.0291933  
    1:     0.451923     -0.370502     -0.741918     -0.328712  
    2:     0.322416     -0.509579      0.100228      0.791411  
    3:     0.252161     -0.514048      0.638283     -0.514553  

  Frobenius norm error in eigensystem A*V-D*V = 1.20349e-12

TEST02
  For a symmetric matrix A,
  JACOBI_EIGENVALUE computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

As a sanity check, input a diagonal matrix.

  Input matrix A:

  Col:          0             1             2             3       
  Row

    0:            4             0             0             0  
    1:            0             1             0             0  
    2:            0             0             3             0  
    3:            0             0             0             2  

  Number of iterations = 1
  Number of rotations  = 0

  Eigenvalues D:

         0:              1
         1:              2
         2:              3
         3:              4

  Eigenvector matrix V:

  Col:          0             1             2             3       
  Row

    0:            0             0             0             1  
    1:            1             0             0             0  
    2:            0             0             1             0  
    3:            0             1             0             0  

  Frobenius norm error in eigensystem A*V-D*V = 0

TEST03
  For a symmetric matrix A,
  JACOBI_EIGENVALUE computes the eigenvalues D
  and eigenvectors V so that A * V = D * V.

  Use the discretized second derivative matrix.

  Input matrix A:

  Col:          0             1             2             3             4       
  Row

    0:           -2             1             0             0             0  
    1:            1            -2             1             0             0  
    2:            0             1            -2             1             0  
    3:            0             0             1            -2             1  
    4:            0             0             0             1            -2  

  Number of iterations = 10
  Number of rotations  = 43

  Eigenvalues D:

         0:       -3.73205
         1:             -3
         2:             -2
         3:             -1
         4:      -0.267949

  Eigenvector matrix V:

  Col:          0             1             2             3             4       
  Row

    0:     0.288675           0.5       0.57735          -0.5      0.288675  
    1:         -0.5          -0.5  -4.44985e-17          -0.5           0.5  
    2:      0.57735   5.05017e-17      -0.57735   -7.0576e-17       0.57735  
    3:         -0.5           0.5   1.86451e-16           0.5           0.5  
    4:     0.288675          -0.5       0.57735           0.5      0.288675  

  Frobenius norm error in eigensystem A*V-D*V = 9.40195e-16

JACOBI_EIGENVALUE_TEST
  Normal end of execution.

17 August 2018 11:19:25 PM